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Censorship

Illegal Prime Number Unzips to DeCSS 307

Posted by CmdrTaco
from the allright-thats-pretty-friggin-clever dept.
Bob9113 writes: "A person named Phil Carmody has found a very interesting prime number. When converted to hexadecimal, the result is a gzip that contains a DeCSS implementation. I've posted a short bit of Java here that takes the prime as a command line parameter and dumps the result to standard out if you want to test it." Very clever, I just wish the background on that page wasn't headache inducing.
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Illegal Prime Number Unzips to DeCSS

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  • by Anonymous Coward
    Please don't spoil the fun of this by posting logical explanations.
  • by Anonymous Coward
    Yeah, true. When I told my mom that there's a prime number that gzip converts to DeCSS source, she immediately cried out: "Then DeCSS can't be illegal".
  • I've always thought that the pursuit of intellectual freedom and freedom of speech was quite dull to begin with myself. Let's all go watch Budweiser ads and eat Doritos.

    Seriously, though, the creativity that's being directed at making a mockery of the DMCA, while not "productive" in the strictest sense of the word, serves at least two important functions:

    1. DMCArt, the more diverse and unrelated it becomes, has a greater liklihood of drawing attention to itself outside the already growing community who know about the DMCA and why it is evil.

    At first, it was a widely distributed piece of illegal code but it had a limited audience and was a very abstract concept. Then somebody sang about it, and made it (while still impenitrable to the average American) a little catchy. I may even have memorized the song accidentally, making my brain illegal. Now people are creating new and more fascinating "interpretations" of DeCSS (almost none of them functionally equivalent to our hero, mind you) each possibly more interesting to another segment of society than the last. Soon, if we're lucky, you'll see CSSDescramble spraypainted on boxcars, and sold to unsuspecting patrons at galleries, and encoded in a pattern of bricks at the base of the latest high rise. That's when you'll know that the DMCA has finally been grepped by America. If people didn't direct their creative juices at this, it would be an unapproachable "Washington thing" (like "insurance,", right Mr. President?).

    2. It keeps people like me from rotting their brain with television for a while, and instead learning more about our craft. That prime number guy likes numbers, so he sits himself down and keeps his tool sharp by finding his own way to say "fuck you" to the DMCA. The guy who wrote the song has a band, and it damn well served a purpose for him beyond mocking the movie studio cabal. So it's not just a noble, necessary thing to criticize the DMCA with art, it's a selfish thing.

    And those are the best things to do of all.

  • by Chacham (981) on Sunday March 18, 2001 @08:42AM (#355841) Homepage Journal
    Will this number now be a prime suspect?

    ---
    ticks = jiffies;
    while (ticks == jiffies);
    ticks = jiffies;
  • Anybody got one which decodes to the Scientology OT secret documents?
  • I think you misunderstood.

    In the interval 1...n there is a finite number of primes.

    Therefore, you can instead of writing down a large prime P, you can write down which number of prime it is in the sequence 1...P.
  • Clearly you haven't considered that anything can be encoded (using prime numbers+gzip, plain gzip, rot-13, whichever encoding you fancy)

    This encoding is no different from any other decoding: It changes information from one representation to another. This is not new - only this particular encoding is new, but the idea of encoding is certainly not new.

    Ok, the rest here is speculation:

    Clearly, gzipping some piece of software does not change the licensing of that software. So, what if I work with numerical simulations and purely by chance my plasma physics data set can be gunzipped into a full distribution of [insert some proprietary software here] ?

    I guess that would be ok, because clearly this happened by chance and I never intended to actually gunzip my data set.

    Likewise, if your key-exchange code by chance generates a prime that just happens to encode some piece of IP, it should be hard for anyone to sue you.

    On the other hand, encoding the "original" for the purpose of distributing it in some alternative representation has always been illegal. gzipping IP doesn't make it legal, neither does encoding it into a prime number after it's gzipped.

    But this is a funny problem ! It puts a new angle on "Intellectual Poverty".
  • by Oestergaard (3005) on Sunday March 18, 2001 @10:54AM (#355850) Homepage
    You're right that anything could be encoded into a prime number (with a suitable prime->original conversion).

    But using some prime->original decoder is no different from say, gunzip. It's decoding of information in on form back to it's "original" form.

    So no, making copies of Win2K is not legal wether it's gzipped or encoded into a prime.

    And distributing DeCSS as a prime number (or gzipped) doesn't change the legality either.

    Subtracting 1 from the number then distributing that number just adds another layer on your decoder, it doesn't change what you're doing. gzipping something twice doesn't remove the licensing restrictions either.

    However, this is interesting because it puts a new angle on the flawed notion of "Intellectual Property" (or, Intellectual Poverty as I like to call it, because that must be what we suffer from if we restrict other's access to ideas that are indeed just mathematics in some form or another).

  • Just wait. You haven't seen encoding all your bases in prime numbers yet...

  • RIAA Petitions Congress To Ban Number Theory
    Mathematicians Declared "Enemy of Intellectual Property (and the American Way)"
    Rambus Patents Prime Numbers

    Any guesses about which one you'll see first? :)

  • The fact of the matter is that every piece of digital information is nothing but a sting of digits.

    Right.

    This one is interesting in that the number happens to be prime.

    The number happens to compress down to a number that can be turned into a prime by adding some trailing digits. This is probably (but not proven AFAIK) possible for any number; what's interesting is that someone tried to do so and was successful.

    My question for a lawyer is this; does Microsoft have legal copyright on some numbers?

    I'm not a lawyer, but the answer is obviously yes: every piece of Microsoft software can be encoded as a (usually multimillion digit) number. Sending that number to someone else would violate copyright law.

    If so, do they also own every number that can be derived mathematically from them?

    No; just because they have a copyright on n doesn't mean they own n - n = 0 or n / n = 1, Onion article [theonion.com] to the contrary.

    You might say they own every number that has to be derived mathematically from them; i.e. gzipping the file, turning it into a prime number, etc. doesn't remove the copyright protection. On the other hand, you could distribute a file containing the first 10^1500 integers, and as long as you didn't also distribute a way of discerning which integers were copyrighted your act should be useless but legal.

    Of course, I'm one of those folks who thinks that the War on Drugs and DMCA are unconstitutional, so if you're actually considering brushing up against the law you should ignore everything I say.
  • But if so, nobody has proved it for Pi or e, at least. I don't know if it's been proven for "starting sequences" of prime numbers.

    Beware of two things you're doing here: you're imagining that primes, Pi, and e are all sequences of "random" digits. They certainly look that way, but it isn't true, and some of that non-randomness may, for example, prevent a particular number from ever appearing in the digit sequence. Secondly, you're trying to make a mathematical argument from "common sense" rather than from axioms and logic. That doesn't work as often as you'd wish it would; common sense sucks.
  • You're missing the point. Your car _has_ a number. Your car isn't a number. I am not stealing your car by emailing my friend your VIN. Ideas _can't_ be owned. That's all there is to it. The basis of copyright law even says that copyright is a gift of the public to the author for the purposes of advancing the useful arts, not a mandate of nature like personal property. The reason that ideas/nonmaterial things can't be owned is that the transfer of copies does no direct harm to the original owner.
  • At least one version of the story can be found in Martin Gardner's "Aha! Gotcha!" (ISBN: 0716713616), 1982.

    Although for this particular story, you pretty much covered it. I've always liked that one though, impossible though it is.
  • 1 is neither a prime nor is it a composite. Same goes for zero.
  • infinity consisting of numbers ending with two is the exact same as infinity which is divisible by 1/16. it is infinite.
  • They couldn't trademark '80486' because it's a part number, and any other manufacturer could also call their chip an '80486'. Just like different word-processor makers can come out with version 7.0 at the same time.

    Actually the original post was closer. You cannot trademark or copyright letters or numbers in the U.S. This was settled back in the '80's by a case (cases?) involving Zilog.

    Remember Zilog, makers of the fine Z-80 microprocessor? Well, they had this Z-80, used in a bunch of CP/M machines of the time, like the TRS-80. Anyway, to protect the name of their product, they essentially attempted to sue everyone on the planet who had ever used the letter "Z". They lost.

    End of history lesson.
  • That's pretty funny. Maybe someday you'll have the balls to put a name to your words.

    So for example, "P" isn't a registered trademark of Parsons in computer systems?

    Yes, shitbag, that's exactly what I'm saying. You cannot trademark a letter, even the letter "P", even if you're Parsons Technology. What Parsons has registered is a trademark for their particular stylized design, incorporating the letter "P". So if I want to call my computer company "P Computers" or even "P Software", then there's nothing they can do about it. Now, were I to call my company "P Technology" and use a "P" logo that was suspiciously similar to theirs, like the one in their trademark record (serial #74179529 registration #1734490, which you can find by searching TESS [uspto.gov]), which by the way clearly indicates that it is for "words, letters and/or numbers IN STYLIZED FORM", THEN they might have a case of infringement.

    If you don't think so, then let me announce that I am applying for a trademark on the letter "E", with respect to its use in all correspondence, electronic or otherwise, to protect my forthcoming product, named "E-Mailer". But I'll license it to anyone who wants to use "E", for the low, low fee of $0.50 per occurrence. Cash only, please.
  • It does help explain the absurdity of the ruling, though. This number is illegal, and you may not display this number, or link to sites that display it. Which number will be next? 626529876? 354157647732?

    You bastard, you told me you burned those pictures and the negatives!

    Numbers by themselves are data. Without context, they do not convey information.
    --
  • 67, 109, 100, 114, 84, 97, 99, 111, 32, 109, 111, 108, 101, 115, 116, 115, 32, 98, 97, 98, 121, 32, 115, 101, 97, 108, 115, 33

    (I don't have a bigint package handy to shift 'em all into an int)

    Decode in ascii and you get "CmdrTaco molests baby seals!". Hey, they're just numbers, so I guess a forged document like a police record rap sheet showing all sorts of other illegal perversions he engages in, discreetly slipped to all his friends, wouldn't be libel as long as I gzipped it.
    --
  • Nope. I also live in a quite predominantly Slavic community...
  • There are already a few "forbidden numbers"

    Note the Orthodoxes are against many countings and IDs because in some of them may appear the idoneous "666".

    13 floor is non-existent in some places with predominant anglo-saxon population

    2 is also for some cultures a "forbidden" or "bad" number. Btw never give two flowers to a girl from slavic culture.

    Some think that the square root of two and pi were "demonic" numbers for Pitagorics, a mysthical sect of Antiquity and predecessors of many Christian ideas and with some love to play maths. The fact of the existence of real numbers was felt as a "fault" in the building of the Universe... Btw Pitagorics were responsible for the advent of prime numbers.
  • Those sentences don't specify order. The first sentence simply says that he found a number, and it doesn't say how. (Your idea as to his process would qualify as "found", IMO.) The second sentence simply explains what the prime number is.

    So, I guess what I'm saying is, yeah, that's probably what happened, but so what?
  • by crow (16139) on Sunday March 18, 2001 @09:04AM (#355881) Homepage Journal
    This is very easy.

    If you want to find something in a prime number, you figure out what you're looking for--in this case, the gziped code. You then search for prime numbers that start with those digits. Since there are an infinite number of prime numbers, you will always be able to find one (given enough time).

    You could also find DeCSS gzipped in a section of Pi or e, based on similar ideas.
  • Barbie should be thrilled!

    --
  • by wavelet (17885) on Sunday March 18, 2001 @09:47AM (#355888)
    Inspired by Phil's effort, a prime number [cmu.edu] encoding of the source of efdtt.c [cmu.edu] has been contributed by Charles M. Hannum.
  • That should be
    x < B^n
  • by platypus (18156) on Sunday March 18, 2001 @09:20AM (#355892) Homepage
    You then search for prime numbers that start with those digits. Since there are an infinite number of prime numbers, you will always be able to find one (given enough time).

    Wrong.

    Tell me the number out of all odd numbers ending with 2. Or take all numbers which don't contain the digit 9 and ...

    Just because something is infinite doesn't mean it contains everything.
    One had to prove that for every number N there existed n, x such that

    P = N*B^n + x

    where x B^n and B is the base (10 for decimal, 16 for hexadecimal etc...).
    I for one am not sure whether this is true or not. I guess it's true and could be proved analogous to the basic proof that there are infinite primes.

  • The idea that all IP is just "numbers" and can't be owned is a fallacy. My car has a number, and I most certainly can own it.

    Even though you're probably a troll, i'll address this. Your car may have a VIN number, but you don't own that number. I can publish that number, and that doesn't mean i'm stealing it from you.

    Copyrighting a number may make sense: the task of -finding- the number that happens to be the source to win2000 is very very difficult for mankind to do. First mankind has to write Win2000. To compensate Microsoft for undertaking this task, the government gives them temporary rights to control the distribution of this number. While i think this time period should be about five years instead of several dozen, it makes sense.

    But to say that someone else cannot distribute a number which THEY have undertaken the task of finding makes no sense.

    --

  • What really happened was most certainly the reverse. He took gzip that contained DeCSS, converted it to hex and analyzed the number.

    Redundant. It says this right there in the link [utm.edu].

    The good geek karma dictated that this number should be a prime and the rest is now the history

    Uninformed. You obviously were in such a hurry to post your message that you didn't actually follow the link [utm.edu], where it clearly explains the formula he used to turn the code into a prime:

    First Carmody took the original anonymous version of the DeCSS C-code and gzip'ed it... By Dirichlet's theorem on primes in arithmetic progression, we know that for each fixed integer b relatively prime to k, there are infinitely many primes ak+b. For technical reasons, if we choose a to be a power of 256 larger than b, the resulting number can still be unzipped to get the original file. This means there are infinitely many prime numbers which yield the same code. These include: k*256^2+2083 and k*256^211+99.

    --

  • by mTor (18585) on Sunday March 18, 2001 @08:47AM (#355896)
    A person named Phil Carmody has found a very interesting prime number. When converted to hexadecimal, the result is a gzip that contains a DeCSS implementation.

    The odds of this happening in this order are slim to none. If you believe in this chain of the evenets I have some stock to sell you. What really happened was most certainly the reverse. He took gzip that contained DeCSS, converted it to hex and analyzed the number. The good geek karma dictated that this number should be a prime and the rest is now the history =)
  • > Some think that the square root of two and pi were "demonic" numbers for Pitagorics, a mysthical sect of Antiquity and predecessors of many Christian ideas and with some love to play maths. The fact of the existence of real numbers was felt as a "fault" in the building of the Universe... Btw Pitagorics were responsible for the advent of prime numbers.

    FWIW, one of the oldest known conspiracy theories claims that Pythagoras was drowned by his own followers in their outrage at his discovery of irrational numbers.

    --
  • by mindstrm (20013) on Sunday March 18, 2001 @09:04AM (#355898)
    It's not that simple.

    They couldn't trademark '80486' because it's a part number, and any other manufacturer could also call their chip an '80486'. Just like different word-processor makers can come out with version 7.0 at the same time.

    And as any type of data can be converted to 'just a number'.... this won't hold up. It's still decss, just encoded and padded out to a prime.
  • by dutky (20510) on Sunday March 18, 2001 @09:35AM (#355899) Homepage Journal
    This can be persuaive because it shows a way to use a computer program (gzip) to circumvent CSS when that program was clearly never intended as a circumvention method in the first place. This is an attack on DMCA in the broad, rather than on CSS and MPAA in particular.
  • by YoJ (20860)
    I'm guessing that the gzip format allows extraneous bytes at the end of the file that don't affect the unzipped output. So he probably added padding to make it a prime, since it is unlikely that the hex number happened to be prime itself.
  • by Saint Nobody (21391) on Sunday March 18, 2001 @09:00AM (#355901) Homepage Journal

    as i recall, numbers alone can never be considered intellectual property. that's what bit intel in the ass with the 486. all the companies that made knockoffs were calling them 486's, diluting the namespace. so intel came out with "pentium" to solve that problem.

    the question now is whether the courts would consider this just a number, or an encoding of the decss data into a number.

  • by slashkitty (21637) on Sunday March 18, 2001 @10:32AM (#355903) Homepage
    look at the 2 line program that implements RSA, which many people consider a very challenging thing to crack!
    print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<>

    )]}\EsMsKsN0[lN*1lK[d2%Sa2/d0<X+d*lMLa^*lN%0]ds Xx++lMlN/dsM0
    are you saying that RSA is weaker then CSS because it only takes 2 lines?

  • by abelsson (21706)
    This doesnt change a thing (legally). Guess what? Any binary data can be represented as a decimal number - and therefore this number is as illegal as the original decss.c (according to US courts atleast) The fact that it is a prime doesnt change anything.

    Still wickedly cool though...

    Of course, you can have even more fun with numbers: don't tell the RIAA, but PI and e contains all their past, current and future songs aswell as all copyrighted material that has or will ever exist in any format you wish. Guess PI should be next on their hitlist.

    -henrik

  • To be more correct, it is countably infinite. The number of real numbers between zero and one is uncountable.

    --Ben

  • But wouldn't that number be useless unless you had a table of all 12345... numbers, or else replicated all the computational work yourself?
  • Actually. Why isn't it written in hex in the first place? Just because average Joe mostly uses decimal numbers, doesn't make hexadecimal any less of a number This leaves the fact that the ONLY thing that makes this decss, is gunzip'ing it. Which also means that as the number itself may not be illegal, and gunzip predates CSS by several years. Neither gunzip or the number may be illegal. Can the ACT of gunzipping it be illegal, knowing that the result is DeCSS? Can TELLING people that the number is DeCSS be illegal? It's not in my country anyway...
  • The last four bytes of a gzip file contain the uncompressed size of the stored file. Unfortunately, the page seems to be /.ted, so I can't check that.
  • Say... Does this mean that there is a prime number than when un-gzipped contains the OT-III text?

  • He describes a similar scenario in Anarchism Triumphant [columbia.edu] which is an interesting - if a little flawed - look at intellectual property and free software.

    Then there's 9892454959483. This one is the source code for Microsoft Word. In addition to being "copyrighted," this one is a trade secret. That means if you take this number from Microsoft and give it to anyone else you can be punished. Lastly, there's 588832161316. It doesn't do anything, it's just the square of 767354. As far as I know, it isn't owned by anybody under any of these rubrics. Yet.

    When I first read this I laughed at the concept of a stream of numbers being copyrightable. But that is of course the current case. Of course it would be even more ridiculous that a naturally-occuring prime would be so subversive, wouldn't it?

  • In order to treat the number as a fraction between 0 and 1, you must have an upper limit for the integer result.

    Not even close: 1/x is between 0 and 1 for all x > 1. More efficient schemes are of course possible.

  • by alex@thehouse (43299) on Sunday March 18, 2001 @10:11AM (#355920)
    The fact of the matter is that every piece of digital information is nothing but a sting of digits.

    This one is interesting in that the number happens to be prime.
    (Is this a mathematical trick? If not how on earth did the author make this discovery?)

    My question for a lawyer is this; does Microsoft have legal copyright on some numbers?

    If so, do they also own every number that can be derived mathematically from them?

    If not, can we legally store any copyrighted files with say 1 subtracted from the number?

    (Think of it as insecure encryption with a trivial key and algorithm.)

    And finally if this act would be illegal, then surely as a copyright holder I own rights to all digital data as you can mathematically transform between any two numbers without much difficulty.
  • > I'm guessing that the gzip format allows extraneous bytes at the end of the file that don't affect the unzipped output.

    That would be cheating... A more elegant way would have been to include padding in the uncompressed output: add a space here and there, it doesn't change the meaning of the program, however it does change its gzipped representation... Write a small program that arbitrarily varies spacing of DeCSS in various places, gzips it and checks primality. Stop once a prime number is found. Or try the same with other, less "artificial" changes: choice of variable names, instruction reordering (where it doesn't affect meaning), etc.

    Next exercise would be to take the largest known prime number, add gzipped DeCSS to it, and attempt to find one DeCSS variant where the new number is prime as well. As this is now the new largest known prime number, it will suddenly appear all over the place, and there's nothing the MPAA could do about it... Now, those numbers are so large that traditional primality tests are not practicable. It'll take a math genius to come up with a program that's fast enough for the purpose. But this is actually a blessing: if the primality check algorithm will be sufficiently novel, the whole stunt will be worthy of a peer-reviewed article in a math journal, causing the MPAA yet another headache. Does anybody in the audience have the math background to take up the challenge?

  • Or else, somebody could just say: Hey, look at the sequence of digits of pi starting at mumble mumble bazillions mumble mumble and ending 137142 characters later... and he would be in the clear, because Pi exists naturally, and just "happens" to contain the source code of DeCSS at that place. Truth is, by linking to that place, you revealed the code, which formerly wasn't distinguished from the zillion other code-snippets also contained in Pi...
  • That wouldn't work, because that large prime unzips to exactly one source, which would very likely not do anything useful. Think about it...

    However, altering the source, zipping, and testing for primality takes advantage of the fact that there are very many primes around, so it's highly probably that you will eventually hit one of them. However, the probability of hitting a very specific prime is incredibly small.

  • > Finding a program that factors large prime numbers (or determines if a number is prime)

    These are not the same thing. There are algorithms (based on exponents) which allow to determine (with a certain degree of confidence) whether a number is prime or not without having to factor it. This is by the way the reason why those encryption algorithms are practicable: in order to generate keys, you need prime numbers. Now, the algorithm would not be very useful if it was as difficult to generate a (legitimate) keypair than it would to break one...

  • Equally as unprovable and worthless opinion:

    Exactly as much effort is "wasted" on cynicism as there is on creativity and discovery.

    turns into a positive affirmation of human action and generally makes the world a better place:

    ... but I'm not one to argue that either is more valuable than the other... I value them both. Your cynicism, while irritating and unfounded, serves a purpose too, my child.

    DMCArt is the application of the human mind, as much as advertising, architecture, fornication, or whatever, and is also an explicit rejection of intellectual control by governing bodies or corporate beings--a double whammy if you ask me. Enjoy your aimless cynical life, and I will enjoy my aimless and creative one.

  • by mr100percent (57156) on Sunday March 18, 2001 @09:24AM (#355930) Homepage Journal
    So either God uses Linux, or maybe the MPAA is satanic after all, and he built DeCSS into the universe to make it crumble..

    BTW, doesn't the MPAA's address have the number 666 in it? Or am I thinking of another corp.?

    --Never trust a tech who tattoes his IP to his arm, especially if its DHCP.
  • In blogan's favor though. This the textbook proof that the set of primes are infinite...

    Here's the REAL trick though. People have been talking about countable mersienne (sp!!!) primes, etc.

    Now we just need the set of "illegal primes"! Since they're a subset of primes, they're countable. Are they infinite?

    Or perhaps there's some way to, in a STRICT MATHEMATICAL sense, create a corollary to this that is this specific prime is illegal, then all natural numbers N are illegal. Something a bit more formal than "If N is 'illegal' than 1 is illegal, qed".

    Obviously the number of illegal numbers is infinite, since we can just take compounds of that prime. I don't think you could make an argument that a factor of an illegal number was illegal.

    Can anyone come up with a smaller "illegal" number? Not actually post it, but methods to derive it? If it was fairly small, then all compounds of that number would be illegal
  • by TrevorB (57780) on Sunday March 18, 2001 @10:11AM (#355934) Homepage
    Prime numbers are countable. You in theory can be able to reduce this from 1400+ digits by saying it's the 12345...42153th prime (perhaps about 100 digits).

    However determining this number would be (ludicrously) computionally expensive. Another quest for distributed.net?

    Why work on the CSS code, why not the keys themselves? That would be more interesting.
  • > You're distributing a number. This is why copyright (and intellectual property) law doesn't make sense with digital data.

    Actually they do, but not for the reason you mentioned.

    Yes, you're right, ultimately it DOES come down to just a number, BUT, if an author puts time and effort into creating something, I believe, he should have a) the right to limit how his work is spread, and b) the right to be comensated.

    We should be free to distribute any sequence of digital data as we want, as long as the number is being "interpreted in the proper usage."
    i.e. I need to to send someone a long prime, which also happens to represenet some .mp3. If the number is not being "interpreted" as a song, then no restriction on the transaction should occur.

    Intellectual property rights are neither [freenation.org].
  • Hm. That code looks a bit weird (I haven't tried actually running it, though). The second for loop's body ends with a semicolon, not a comma, and there are no braces to be seen. Still, the following (long) loop is indented. Should it really be? Not that it matters, since this is C and not Python, but if the point is to make it readable... Weird. I just ran it through GNU indent [gnu.org], and it seems to agree. I didn't look at the original (non-cleaned-up) code, either.
  • If DECSS is legal in Canada/Mexico, why not bring the lawsuit up as an illegal trade practice under NAFTA?
  • Is it illegal to distribute numbers when they happen to represent copyrighted/illegal data?

    Yes. This particular prime-encoding method is just another method of data encoding. It changes nothing: all digital data is encoded in binary code, essentially a number.

    I'm also sure it's possible to find a research project/paper which has used a number which represents copyrighted/illegal data (maybe this number).

    First, much less likely than you might think -- you have to understand the sheer scale of numbers. Certainly not this number. Accidentally coming up with this number is no more likely that running a random text generator until it produces the code you're looking for. In theory, this could happen, but in practice it never would. That's the flaw in your reasoning: the problems you bring up exist only on paper and would never actually come up.

    So. Moral reasoning: I know of no real-world moral problems that might arise from encoding data in a slightly different way. If you know of an actual case, please bring it to my attention. Legal reasoning: this is simply a new data encoding and changes nothing. The person who published this obviously had distributing DeCSS as an intent, and therefore broke the law.

  • by fougasse (79656) on Sunday March 18, 2001 @04:08PM (#355949)
    does Microsoft have legal copyright on some numbers?

    No, they don't. They have copyright on some particular piece of source or binary code. This copyright applies regardless of the form in which the code is stored, and applies to obvious derivatives as well.

    Storing a piece of data as an integer is simply a different way of encoding and storing data, like ASCII or EBCDIC. Saying that performing a simple mathematical operation on an integer negates copyright is as preposterous as saying that, say, my novel is copyright when stored in ASCII but public domain when stored in EBCDIC. As to the number-transform question: if you encoded my novel and transformed it into "2", I would certainly not hold copyright on the number 2. That's because you couldn't logically argue that my novel is stored within the number "2". You could write a program to reverse whatever procedure you used to reduce my novel to 2, and when fed 2 it would spit out my novel. In that case, the combination of the data and your program would be illegal, because it's just another way of storing data.

    In other words, as a copyright holder, you hold copyright on all digital data which can reasonably be seen as an encoding of your copyright data. It's quite straightforward, really, and semantic number games never end up meaning anything in the real world.


  • Hmm.. what was that Ayn Rand book called again? Anthem? I used to think the idea was preposterous.

    (Of course, you'd have to exchange the goverment for the corporations and workers for consumers, but the idea is very much the same, if taken to an extreme.)

  • Your car is not your intellectual property.

    If you want to make the analogy more accurate, you would say that a digital 3D model of the design of your car could be converted into a number. But don't be surprised when the data that the number represents, when properly decoded, certainly does belong to some corporation.

    Don't believe me? Go out and make a nearly perfect clone of a 2001 Camero and start selling them for $1000 a pop. See who comes knocking at your door. When your only legal defense is that you used a number to design your car, you will be laughed at and then thrown in jail.

    Your point might be accurate. Your example is not.
  • If your content is 'hello', and you encode that as 08, 05, 12, 12, 15, or 0805121215, then you can make it a number between 0 and 1 by simply prepending a decimal point: 0.08051212150000000...

  • by Speare (84249) on Sunday March 18, 2001 @09:01AM (#355954) Homepage Journal

    There was a short science fiction story that went something like this.

    • Alien arrives on Earth.

    • Alien asks to view all Earth encyclopedias.
      Alien encodes all the content as a single very massive integer.
      Alien treats number as a fraction between 0 and 1.
      Alien takes out a crystal rod, measures, and makes a single mark on it.
      Alien goes home with the rod to decode later.

    Of course, a few terabytes of digits would exceed the resolution of any atomic matter, but the idea was there.

  • but Pi does have a random distribution, stastically speaking. Which means if you look in it long enough, you'll find everything that can be represented by numbers, since it's also infinitely long.

    I wonder if you could represent even one RIAA copyrighted song in the first 64 bits of Pi. Then all you'd have to do would be feed the start and end offsets into that formula and you'd effectively have a compression algo which squashes down to two long-longs. Of course, most interesting stuff is probably farther out and you might have to use more bits to represent the start and end offsets and of course the encoding of your content would take hella long time.

  • Whether something is wrong or not is completely orthogonal to whether or not it can be enforced. Yes, it is ridiculous to ban certain numbers or T-shirts but that doesn't make it ridiculous to ban DeCSS. You aren't proving anything by pointing out that DeCSS can be encoded in a prime number.
  • The smallest gziped binary (Linux ELF, i686) of dcss I was able to build is 1787 bytes long (the original was 3608). I used the 7-line C source that was posted a couple days ago (compiled with -s -O3 -mpentiumpro). I'm sure it's possible to do better... anybody tried?
  • probably did ... however its the best challenge to the DeCSS decision thus far (IMHO), in that it drives home to even non-technical people how absurd the decision was ...

    I can't wait for the t-shirt :)

  • by Tom7 (102298)
    This is nonsense. Not to defend the MPAA, but 7 lines of C code (especially all packed up like that) is enough to represent some very complicated ideas. Given arbitrary-precision arithmetic, for instance, I'm sure you could implement RSA in 7 lines (you can certainly explain it in pseudocode). The RC4 algorithm is probably about 2 lines.

    The brevity of an idea has nothing to do with how useful/important/'honest' it is. For that matter, it doesn't have much to do with how complicated it is. (Can you really explain CSS after "reading" that 7 line program?)
  • I was actually wondering that as well. The problem with DeCSS isn't that it decrypts the data though. Owning it isn't illegal. Giving it to others is illegal, and that's what all of the cases have been about, as far as I know.

    Now, we do run into a weird situation where we XOR together a Linux CD image and a Windows CD image. Techincally, you could claim that you had encrypted your Linux distribution and you should be able to distribute it because it's Linux, only encrypted. Getting Windows out of the image because you already have Linux is just a side effect...

    You could probably argue something similar - that you encrypted Free File X using Copyrighted File Y as the key - and claim that it's not your fault that the key is so easy to reverse engineer. :-)

    This is all hypothetical of course, I actually support copyright in general, although with fair use principles enforced (not simply allowed to be worked around).
  • When I first read this I laughed at the concept of a stream of numbers being copyrightable.

    Umm... ALL software in binary form is just a stream of numbers number, and programs distributed as such have been successfully copyrighted for decades. .mp3's are just a series of numbers which was not even created by the copyright holder, but that's not saving Napster.

    I always wondered if that would be a suitably confusing defense of copyright violation. "No your honor, I didn't 'pirate' this [item]. I merely copied a large series of seemingly random numbers, [refers to printout in binary form] see? It's just a bunch of 1's and 0's, not [item]." The counter arguments would just degenerate into semantics and the whole thing would just get ugly. :-)

    That gets even more weird when you consider that the zipped form of the binary data in no way represents what was originally placed under copyright.

    So, let's say you burn that to a CD. It's just a bunch of invisible pits on a disc. That's copyrighted? Even if you use the proper "device" (i.e. computer) to convert it into "human readable" form, it's still not the copyrighted material. You have to apply a second process to convert the data out of comressed form.

    So, from one perspective (it's just a bunch of pits on a disc!) copyright seems silly. From another (I can see on a computer screen, using data extracted from those pits, an image which says 'Copyright (C) 2000 Microsoft (R)') it seems more reasonable, since you're actually producing order out of what would otherwise be random or imperceivable.

    I wonder what happens if you use the Linux kernel as the XOR "key" to encrypt Windows? &ltow, brain hurt&gt
  • I had a post modded up and down like 8 times, settling eventually on 3.
    ----
  • We'll need a Prime Directive for this number:
    It is a violation of Federal law to use this number in a manner inconsitent with the DMCA.

    --
    EFF Member #11254

  • Well, 1 has two factors. 1 and 1. :-)

    Where 1 is a prime or not is largely a matter of contention. But you certainly cannot call it a composite number, for then all other prime numbers would have to be composite as well.

  • In retrospect, it was only a matter of time 'till something like this happened. Programs are long numbers, and through this method you can now make any program a prime number.

    Much better yet:

    Theorem: For any circunvention method, there exists a prime number that encodes it.

    So wellcome to the world a new class of numbers: Illegal Prime Numbers.

    It's a great day for math!

    cheers!

    rmstar

  • by Dlugar (124619) on Sunday March 18, 2001 @12:53PM (#355987) Homepage

    The formula he used to "find" this prime number can be found here:
    http://www.utm.edu/research/primes/glossary/Illega l.html [utm.edu]
    Basically it says this:

    First Carmody took the original anonymous version of the DeCSS C-code and gzip'ed it (a standard UNIX program for making files smaller). Suppose we call the resulting number k. By Dirichlet's theorem on primes in arithmetic progression, we know that for each fixed integer b relatively prime to k, there are infinitely many primes ak+b.

    For technical reasons, if we choose a to be a power of 256 larger than b, the resulting number can still be unzipped to get the original file. This means there are infinitely many prime numbers which yield the same code. These include: k*256^2+2083 and k*256^211+99. At the time these were found they both were large enough to fit on the list of largest known primes (because of the method of proof).


    Dlugar

  • You have too much faith in the american public.

    Remember: this war will be won by the people who can most easily pander to the irrational stupidity of the non-geek population of this world (case in point: the USPTO shenanegans that have been going on). And, in that sense, since the folks at the MPAA, the RIAA, and any other TLAA (three letter acronym association) appear to have a general intellect that more closely matches that of our barely upright-walking, suit-wearing, pre-neanderthal brethren on this planet, they will win. we will lose. and i, my friend, will continue to break the laws made by them without any loss of sleep.


    FluX
    After 16 years, MTV has finally completed its deevolution into the shiny things network
  • Funny thought - I forget where on the net there is a searchable database of the first million numbers in PI - so if I search PI for this string of numbers, would that make PI illegal too?
  • :)

    So what happens if i find a prime which happens to unzip to Stan by Eminem, or Scientology secrets, or a list of spies, or whatever?

    What i someone set up Primster - a site which allows users to trade prime numbers. How hard is it to find these primes?
  • Great now when you buy those text books they'll cost more 'cos the MPAA is gonna want to put a fee on it because it could be used as a piracy tool. This is gonna kill the used text book market, that'll be illegal.

    I'm gonna go start work on "Texter" an internet text book trading programme.

  • The idea that all IP is just "numbers" and can't be owned is a fallacy. Anything in the universe can be hashed to a numerical representation. My car has a number, and I most certainly can own it. To suggest otherwise is to advocate a communist system.

    If you really believe that all IP is just a number, you are welcome to develop software by spewing bignums into a buffer and executing them to see whether or not they are useful.

    See you in a googol years.

  • First Carmody took the original anonymous version of the DeCSS C-code and gzip'ed it (a standard UNIX program for making files smaller). Suppose we call the resulting number k. By Dirichlet's theorem on primes in arithmetic progression, we know that for each fixed integer b relatively prime to k, there are infinitely many primes ak+b. For technical reasons, if we choose a to be a power of 256 larger than b, the resulting number can still be unzipped to get the original file. This means there are infinitely many prime numbers which yield the same code. These include: k*256^2+2083 and k*256^211+99. At the time these were found they both were large enough to fit on the list of largest known primes (because of the method of proof).
  • Ok. Perhaps I was using a slightly inaccurate definition of irrational numbers, but my point is that for number such as e and pi, which are naturally derivable as opposed to the construct you describe, do possess this property.

    That's probably not entirely clear, so I will explain what I mean by calling your number a construct. The algorithm you describe does not really generate a number. It generates a string of digits. If you convert the number corresponding to this string of digits to a different base, your pattern vanishes. Thus it is not really a natural pattern, but a coincidence created by working backwards, kind of like the images in the gallery of DeCSS decoders that just happen to have the gzipped code embedded in them. You have created a very interesting coincidence, but it's like saying that because you can build a Pentium III from elements found in nature, that Pentium IIIs are naturally occurring. Even Douglas Adams would grimace at that one.
  • by ca1v1n (135902) <snook@NETBSDguanotronic.com minus bsd> on Sunday March 18, 2001 @10:11PM (#356001)
    Transcendental numbers like Pi and e, while not being random, are indeed patternless. Given a sufficiently long string of digits (quite possibly longer than one could encode on a hard drive the size of the earth), one could eventually happen upon any given 1401 digit number they were looking for. I am guessing that the same holds true for all irrational numbers. I do suspect that the conversion to hex would be a little different, (Have you ever tried converting non-whole numbers to another base? It's a bit of a pain in the rear.) but you'd find it there too. If you search pi over a long enough range, you can find your phone number, your IP, your birth date, or the build ID for your browser. You can even find some rather long strings of zeros. There are websites for this. In fact, if you want, there are places where you can download pi ten megabytes at a time, and search yourself. Try it out. Do a statistical analysis. I suspect you'll see results very similar to those for random numbers.
  • IIRC, you cannot express irrational numbers using the Roman counting system. The Romans understood division & multiplication; but zero, place notation, and the decimal point were unknown in Europe, the Middle East, and Africa until Arabic astrologers adopted and formalized the older Hindu counting system sometime around 662 CE. The Hindus were using a base-10 place notation system as early as 3000 BCE. There's a particuarly interesting article about the history of counting systems here [wlv.ac.uk]
  • Fool. Of course it changes the legality !

    This prime number _IS_ deCSS. The MPAA will either have to ban this prime number, ban gzip, or ban anyone from telling people that the number is deCSS.

    Either way, I don't see this getting through the courts, even in the US...

  • Wouldn't that be 2^1401? If you can find a hard drive that can store that many bytes, please don't bring it anywhere near me, I'm allergic to those kind of gravitational fields. They make me compress.
    --
  • I think what the poster meant was that if you had a rod a mile long, you would be able to record more data on it then a rod an inch long, beacuse you could get a more precise mesurement.

    Rate me on Picture-rate.com [picture-rate.com]
  • > How many 1400 digit primes exist?

    A little less than 10 times the amount of less than 1400 digits ones.

    Looks like geeks have troubles understanding what entropy is. Face it, you'll not going to get this number much smaller than 1400 digits, no matter how hard you try it.

    Cheers,

    --fred

  • by f5426 (144654) on Monday March 19, 2001 @04:29AM (#356012)
    > This one is interesting in that the number happens to be prime.

    It isn't even remotely interesting. There are a *lot* of prime numbers. About one on 3000, for a 1400 digits number.

    Considering how easy it is to build valid variation of a gzippped file, it is a one banana thing.

    Even if gzip would not accept any variation (ie: if a source file could give only one gzip file, and if any alteration would produce an error at output), then modify the C source file would be just too easy (put a '/*n*/' at the begining, and compress for n incrementing from zero. Would take about 1500 try), unless gzi pformat could never give you a prime number (ie: always finished with a binary '0')

    Now, what is the size of w2k source code ? 1 Gygabyte ? There are prime numbers about every few billions in that range. By messing with 4 bytes (!) of the source, you can have resonable expectation that you can make the result a prime number (if windows source code ends with a binary '1', of course).

    Cheers,

    --fred
  • by napolium (144862) on Sunday March 18, 2001 @11:44AM (#356013) Homepage
    Then you should be able to find the prime number you just found in the prime number you just found. Or can you find Pi and Pi... hmmm?
  • by Dyolf Knip (165446) on Sunday March 18, 2001 @10:07AM (#356036) Homepage
    Courtesy of Segfault [segfault.org].

    Open Source Transcendental Constant

    In a revelation that could rock the foundations of science, a researcher in Pennsylvania has discovered that the digits of the transcendental constant PI encode a version of the Linux kernel. "I can't believe it," the researcher, Neil Hoffman, exclaimed. "And yet, here I am staring at what appears to be the source code for Linux kernel 5.0.0. Needless to say, my whole world-view has changed..."

    Hoffman made the discovery accidentally. "I was trying to write a more efficient algorithm in C to calculate individual digits of PI. However, my relative lack of programming experience, combined with C's highly obfuscated syntax, led me to the discovery. Instead of calculating each digit and returning it as an int, my program was (for some reason I still haven't been able to figure out) converting it to its ASCII equivalent and returning it as a char."

    "Then it hit me. What if some kind of secret messages, encoded in ASCII, was stored in the digits of PI? I set to work on the problem, and after several months of toil, have discovered the awesome truth. My algorithm, which applies several dozen conversions and manipulations of each digit of PI, spits out plain vanilla ASCII characters that happen to form the source code for the Linux kernel."

    "I tried to compile the source code, but gcc choked on it. Apparently a later version of gcc is needed to compile the Linux 5.0.0 source code. It's too bad the code for gcc isn't encoded in another transcendental constant. Or is it? I wonder what would happen if I fed e through my algorithm..."

    Many scientists are skeptical about Hoffman's discovery. One mathematician who has memorized the digits of PI to 10,000 places said, "This is the kind of nonsense one would expect to find in a tabloid such as the National Mathematics Enquirer. Or a nerd humor site. Hoffman's discovery' is obviously a hoax designed to secure government research grants."

    Another scientist Segfault contacted said, "Hoffman's claim is filled with holes large enough to push Windows 95 through. Apply a little critical thinking and look at all the inconsistencies and problems with Hoffman's discovery'. ASCII is an arbitrary code. Why not EBCDIC? Also, the base 10 number system, which his PI-to-ASCII scheme is based on, is arbitrary. Why not binary numbers? Oh, and then there's the biggie: PI is infinitely long. The Linux source code is not (Windows NT, on the other hand...). Explain that, PI Boy!"

    Hoffman will formally present his findings to the scientific community on March 14th at the Annual PI Day Conference and Exposition in Chicago. One conference attendee said, "Usually the PI Day expo is pretty boring, with some asinine workshops about 'The History of PI' and Teaching Techniques to Make Learning About PI More Fun for Remedial High School Students'. However, with the unfolding brouhaha surrounding the Linux-PI connection, this could be a very interesting convention. Then again, there's going to be several hundred mathematicians from around the world in attendance. It might not be that exciting after all."

    In a related matter, Segfault has received an unconfirmed report that a region of the standard Mandelbrot fractal contains what appear to be the words "LINUS TORVALDS WAS HERE". In addition, the words "TRANSMETA: THIS SECRET MESSAGE IS NOT HERE YET" supposedly appear within the depths of the Julia Set.

    Linus Torvalds and Benoit Mandelbrot were unavailable for comment at press time.

    --

  • by fatphil (181876) on Sunday March 18, 2001 @01:52PM (#356060) Homepage
    There is an intricate mathematical reason why I did it without the tables. In short - the number is too damn big to prove _formally_ (I am a mathematician) using Elliptic Curve Primality Proving (ECPP), due to the O(n^6) runtime.

    In my favour is the precedent set by the Think Geek T-shirt which has no tables either. Unless you're talking about the one with only tables, and that has no code. If ThinkGeek have an illegal T-shirt, then my prime number is just as illegal.

    FatPhil
    --
  • by Erasmus Darwin (183180) on Sunday March 18, 2001 @11:09AM (#356063)
    Your recipient has the message and all you transferred was two completely unrelated numbers.

    You seem to have an odd definition of "unrelated". "Extract a sequence of pi starting at position X and continuing to position Y." is a fairly simple function, that can be defined as a decryption scheme. The numbers you find into that scheme are your encoded message and the result is your message. Just because your formula uses pi doesn't make your input unrelated to your output.

    On the other hand, XOR does allow for some confusion. Imagine I take a purely random file (based off of measuring radioactive decay or some such) and then XOR it with DeCSS. Now I've got my random file and my encrypted DeCSS -- the catch is that there's no way to tell which is which. If I've got both files, I can XOR them and get DeCSS, but otherwise both files look like random noise and both files are treated "equally" by the decryption process.

    To make things even more interesting, imagine two people, named Bob and Ted, who have online collections of files with random numbers in them. Now let's say Ted's a bit of a free speech advocate. So he takes a copy of DeCSS, XORs it with one of Bob's random number files, and posts it to his site as a collection of random numbers. How do you prove that it's Ted who's hosting the copy of DeCSS and not Bob? What if you force Bob to remove his set of random numbers, when someone else had used that set as an XOR decryption key for something else? What if that person had both the encrypted and unencrypted versions available (say, as a demonstration of using XOR to encrypt a file)? Using the encrypted and unencrypted versions for the third party, you could recreate Bob's (removed) key. Then you could use that key to decrypt Ted's encrypted DeCSS.

  • by Mr. Polite (218181) on Sunday March 18, 2001 @09:13AM (#356088)
    The article says that the source is "Sans Tables".. in other words, it's useless. So what's the point? Isn't it the encryption keys that are actually the "trade secrets" in question?
  • by kosipov (218202) on Sunday March 18, 2001 @08:52AM (#356089)
    Math haters rejoice! Theory of prime number is now illegal under Digital Millenium Copyright Act.
  • Ah, but you forgot something:
    4856. . .74
    66699. . .7166639. . .9966669. . .8766689. . .4766629. . .9443

    Clearly, this is not a holy number. I predict that tomorrow's headline shall be Catholic Church Denounces DeCSS.

    (Lameness filter, filter thyself! It's not an awful long string of letters, it's a number. It's not in all caps, it's a number. A number is a character with an ASCII value in the range of 48 to 57. Capital letters are from 65 to 90. Got it?)

  • by Joey7F (307495) on Sunday March 18, 2001 @09:13AM (#356115) Homepage Journal
    The MPAA has issued a statement on the article posted by /. "All your base 16 are belong to us" --Joey
  • by Cryogenes (324121) on Sunday March 18, 2001 @12:07PM (#356130)
    A good approximation to pi(x), the number of all primes below x, which was first given by Gauss is obtained by taking as starting point the empirical fact that the frequency of prime numbers near a very large number x is almost exactly 1/log x. From this, the number of prime numbers up to x is approximately given by the logarithmic sum Ls(x) = 1/log 2 + 1/log 3 + ... + 1/log x which can be bounded from below by x/log x. So, if x has 1400 digits, the number of primes below x will have 1397 digits, give or take one. So you could save three bytes. Surely a contender for the prize for the most gratuitous use of all cpu time until the end of time.

"Just think of a computer as hardware you can program." -- Nigel de la Tierre

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